The London mayor said that along with a number of other Labour MPs and mayors, he would be lobbying party leader Sir Keir Starmer to scrap the cap, which he argued is piling further pain on families struggling with the cost of living crisis.
Mr Khan was careful to avoid criticising Sir Keir however, saying that he “understands why” the party is not committing to removing the cap, given the state of the UK economy.
The cap, which came into force in 2017, restricts child tax credit and universal credit to the first two children in a family, with only a few exceptions.
The Child Poverty Action Group estimates removing the limit would cost £1.3bn a year but would lift 250,000 children out of poverty overnight.
Mr Khan said: “There are families with not just one or two children, but those in particular with more than two children, who are really struggling with the cost of living crisis.”
“The Government’s benefit changes are having an additional negative impact on those families just about keeping their head above water, relying upon food banks and the support of faith communities, City Hall and others, to survive. I think this policy should be changed.”
He added: “But I completely understand why we’re having this conversation. It’s a consequence of the Tories’ mismanagement of our economy.
“It’s a consequence of them messing up the Government’s finances, so I can understand why Keir Starmer and [shadow chancellor] Rachel Reeves can’t automatically promise a reversal of this.
“It’s incredibly important to recognise that it’s possible to be in favour of changing this policy but also wanting to make sure that there’s money in the kitty to pay for this policy.”
Asked whether he will be telling Sir Keir for the change to be made, the mayor said: “I’m quite clear that there are number of things that a new Labour government would want to do, which they will not be able to do because of the Tories’ mismanagement of the economy.
“All of us will have a list of priorities we’d like a new Labour government to do, and I’ll be lobbying the Labour team on this issue and a number of other issues, as I do all the time.”
Sir Keir told the BBC’s Sunday with Laura Kuenssberg the policy would not change under a Labour government.
Although he did not give a reason during the interview, members of his shadow cabinet said it was because this would constitute an unfunded spending commitment.